260 research outputs found
Gauge invariance in Loop Quantum Cosmology : Hamilton-Jacobi and Mukhanov-Sasaki equations for scalar perturbations
Gauge invariance of scalar perturbations is studied together with the
associated equations of motion. Extending methods developed in the framework of
hamiltonian General Relativity, the Hamilton-Jacobi equation is investigated
into the details in Loop Quantum Cosmology. The gauge-invariant observables are
built and their equations of motions are reviewed both in Hamiltonian and
Lagrangian approaches. This method is applied to scalar perturbations with
either holonomy or inverse-volume corrections.Comment: 16 page
Anomaly-free perturbations with inverse-volume and holonomy corrections in Loop Quantum Cosmology
This article addresses the issue of the closure of the algebra of constraints
for generic (cosmological) perturbations when taking into account
simultaneously the two main corrections of effective loop quantum cosmology,
namely the holonomy and the inverse-volume terms. Previous works on either the
holonomy or the inverse volume case are reviewed and generalized. In the
inverse-volume case, we point out new possibilities. An anomaly-free solution
including both corrections is found for perturbations, and the corresponding
equations of motion are derived.Comment: previous mistake corrected leading to new result
Primordial tensor power spectrum in holonomy corrected Omega-LQC
The holonomy correction is one of the main terms arising when implementing
loop quantum gravity ideas at an effective level in cosmology. The recent
construction of an anomaly free algebra has shown that the formalism used, up
to now, to derive the primordial spectrum of fluctuations was not correct. This
article aims at computing the tensor spectrum in a fully consistent way within
this deformed and closed algebra.Comment: 5 pages, 6 figures, accepted by Phys. Rev.
Observational issues in loop quantum cosmology
Quantum gravity is sometimes considered as a kind of metaphysical
speculation. In this review, we show that, although still extremely difficult
to reach, observational signatures can in fact be expected. The early universe
is an invaluable laboratory to probe "Planck scale physics". Focusing on Loop
Quantum Gravity as one of the best candidate for a non-perturbative and
background-independant quantization of gravity, we detail some expected
features.Comment: 75 pages, invited topical review for Classical and Quantum Gravit
Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves
Loop quantum cosmology provides an efficient framework to study the evolution
of the Universe beyond the classical Big Bang paradigm. Because of holonomy
corrections, the singularity is replaced by a "bounce". The dynamics of the
background is investigated into the details, as a function of the parameters of
the model. In particular, the conditions required for inflation to occur are
carefully considered and are shown to be generically met. The propagation of
gravitational waves is then investigated in this framework. By both numerical
and analytical approaches, the primordial tensor power spectrum is computed for
a wide range of parameters. Several interesting features could be
observationally probed.Comment: 11 pages, 14 figures. Matches version published in Phys. Rev.
Non-singular Ekpyrotic/Cyclic model in Loop Quantum Cosmology
We study the role of non-perturbative quantum gravity effects in the
Ekpyrotic/Cyclic model using the effective framework of loop quantum cosmology
in the presence of anisotropies. We show that quantum geometric modifications
to the dynamical equations near the Planck scale as understood in the
quantization of Bianchi-I spacetime in loop quantum cosmology lead to the
resolution of classical singularity and result in a non-singular transition of
the universe from the contracting to the expanding branch. In the Planck
regime, the universe undergoes multiple small bounces and the anisotropic shear
remains bounded throughout the evolution. A novel feature, which is absent for
isotropic models, is a natural turn around of the moduli field from the
negative region of the potential leading to a cyclic phenomena as envisioned in
the original paradigm. Our work suggests that incorporation of quantum
gravitational effects in the Ekpyrotic/Cyclic model may lead to a viable
scenario without any violation of the null energy condition.Comment: 24 pages, 11 figures. Additional numerical results discussed to show
robustness of non-singular bounce of the scale factor and turn-around of the
moduli field. References added. To appear in Physical Review
Consistency of holonomy-corrected scalar, vector and tensor perturbations in Loop Quantum Cosmology
Loop Quantum Cosmology yields two kinds of quantum corrections to the
effective equations of motion for cosmological perturbations. Here we focus on
the holonomy kind and we study the problem of the closure of the resulting
algebra of constraints. Up to now, tensor, vector and scalar perturbations were
studied independently, leading to different algebras of constraints. The
structures of the related algebras were imposed by the requirement of anomaly
freedom. In this article we show that the algebra can be modified by a very
simple quantum correction, holding for all types of perturbations. This
demonstrates the consistency of the theory and shows that lessons from the
study of scalar perturbations should be taken into account when studying tensor
modes. The Mukhanov-Sasaki equations of motion are similarly modified by a
simple term.Comment: 5 page
Singularities in loop quantum cosmology
We show that simple scalar field models can give rise to curvature
singularities in the effective Friedmann dynamics of Loop Quantum Cosmology
(LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker
cosmologies with a canonical scalar field and a negative exponential potential,
or with a phantom scalar field and a positive potential. While LQC avoids big
bang or big rip type singularities, we find sudden singularities where the
Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude
that the effective equations of LQC are not in themselves sufficient to avoid
the occurrence of singularities.Comment: 5 pages, 3 figures. v2: Comments and references added. v3: Minor
additions, version to appear in PR
- …